Kinematic Analysis and 3D Workspace Development of 3DOF Parallel Manipulator with a Rotary Base

This paper presents the systematic methods to deal with kinematic analysis of 3-PRS configuration parallel manipulator involving non-linear simultaneous equations. Using the loop closure constraints, three coupled equations are formulated using configuration of the manipulator. Bezout’s resultant and Sylvester method are used to determine roots of three non-linear equations. The tilt of the moving platform is measured with respect to fixed base for single prismatic joint actuation or any combination of these three joints actuations. The maximum tilt of moving platform for the proposed configuration is also computed for limited range of joints. Tool tip coordinates are determined using vector approach with reference to established coordinate system on the base platform. Jacobian matrices are derived for active and passive variables for singularity determination. Using tool tip coordinates for various combinations of linear actuations as point cloud, workspace for 3 – DOF parallel manipulator is developed. Keywords— Parallel manipulators, Bezout’s resultant, Jacobian, Singularity, Workspace